Albert C Chaney 21 February 2008 Dynamics and

Albert C. Chaney 21 February 2008 Dynamics and Control Spin Stabilization of Third Stage AAE 450 Spring 2008

Spin Stabilization § Cone with changing mass properties § Constant T and mass flow rate § Max Vanguard Thrust misalignment 0. 5 deg § Misalignment causes moment that spinning can average out § Vanguard designed against a 0. 25 degree (4. 4 mrad) velocity pointing error AAE 450 Spring 2008 Group Name (i. e. Trajectory

Spin Required § Velocity pointing error aligned with average angular momentum vector orientation 1 § Vanguard spun at a minimum of 150 rpm § To achieve pointing error of 4. 4 mrad must spin 300 rpm Future Work § Determine methods to achieve spin AAE 450 Spring 2008 GNC

References § § Longuski, J. M. , Kia, T. , and Breckenridge, W. G. , “Annihilation of Angular Momentum Bias During Thrusting and Spinning-up Maneuvers, ” Journal of the Astronautical Sciences, Vol. 37, No. 4, 1989, pp. 433 -450 http: //www. astronautix. com/lvs/vanguard. htm AAE 450 Spring 2008 DNC

Backup Slides AAE 450 Spring 2008 DNC

Backup Slides Vanguard Test Rocket r (m) 0. 25 h (m) 2 1. 233 31 184. 5 11562 835. 7 Initial Mass (kg) 210 81. 34 Mass Flow Rate (kg/s) 5. 1243 0. 276 Thrust Misalignment (deg) 0. 5 rpm 150 300 Burn Time (sec) Thrust (N) AAE 450 Spring 2008

Inertia Properties Euler’s EOMs Kinematical Equations Moment Calculation r is radius of cone h is height of cone AAE 450 Spring 2008